Two-Dimensional Collisions and Conservation of Momentum

Vocabulary terms and definitions covering linear and two-dimensional momentum, collision types, energy loss, and particle scattering.

Impulse Formula

The expression relating the change in momentum to the net applied force over an elapsed time interval: $\Delta p = F_{\text{net}} \Delta t$.

Linear Momentum Formula

The mathematical product of an object's mass and its velocity: $p = m v$.

Newton's Second Law (Momentum Form)

The law stating that the net external force acting on an object equals the rate of change of momentum over time: $F_{\text{net}} = \frac{\Delta p}{\Delta t}$.

Law of Conservation of Momentum Equation

The principle stating that the total momentum before and after an isolated interaction remains constant: $p_{\text{initial}} = p_{\text{final}}$ (or $\sum p_i = \sum p_f$).

Head-to-Tail Method

A graphical procedure for vector addition where the tail of each subsequent vector connects to the head of the previous vector to construct the resultant.

Resultant Vector

The vector obtained by adding two or more component vectors together, representing the hypotenuse in orthogonal vector addition.

Resultant Momentum Formula (2D Perpendicular Collision)

The magnitude of total momentum resulting from two orthogonal momentum vectors: $p_{\text{final}} = \sqrt{(p_x)^2 + (p_y)^2}$.

Directional Trajectory Angle Formula

The formula used to determine the angle of resultant momentum relative to the horizontal axis: $\theta = \arctan\left(\frac{p_y}{p_x}\right)$.

Elastic Collision Condition

A collision criteria where mechanical kinetic energy is fully conserved: $\text{KE}_{\text{initial}} = \text{KE}_{\text{final}}$.

Inelastic Collision Condition

A collision criteria where kinetic energy is converted into non-mechanical forms such as heat and sound: $\text{KE}_{\text{final}} < \text{KE}_{\text{initial}}$.

Perfect Inelastic Collision Final Velocity Formula

The final velocity expression when colliding objects stick together and move as a combined mass: $v_f = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}$.

Kinetic Energy Loss Formula

A positive scalar measuring the difference between initial and final kinetic energy: $\text{KE}_{\text{loss}} = \text{KE}_{\text{initial}} - \text{KE}_{\text{final}} = \frac{1}{2} m_1 (v_1)^2 - \frac{1}{2} m_2 (v_2)^2$.

Point Mass

An idealized physical body with all its mass concentrated at a single coordinate point in space, with zero geometric volume or rotational complexity.

Scattering Effect

The phenomenon in which colliding point particles deflect and disperse along distinct angular paths due to off-center collision parameters.

Compton Scattering Experiment

A laboratory procedure where particle beams are directed at targets, causing measurable angular deflection and momentum exchange.

Horizontal Momentum Equation for 2D Point Mass Scattering

The conservation of momentum expression along the horizontal axis when the target mass is initially at rest: $m_1 v_1 = m_1 v_1' \cos(\theta_1) + m_2 v_2' \cos(\theta_2)$.

Vertical Momentum Equation for 2D Point Mass Scattering

The conservation of momentum expression along the vertical axis when initial motion is purely horizontal: $0 = m_1 v_1' \sin(\theta_1) + m_2 v_2' \sin(\theta_2)$.